If you're significantly delayed on your last leg it might be worth saying it's a "trip in vain" in that you're so delayed that the reason for your trip will have passed by the time you get there.

I had something similar once (admittedly about 6 years ago) where I ended up in Terminal 3 at Heathrow following a late inbound and there was actually no point in me proceeding to my ticketed destination.

There was a BA senior manager in the lounge at the time - I explained the situation to him which he described as a trip in vain and I did get a refund for that sector.

I don't know if BA still works within this kind of policy in any way though?